This question about genetics (not required reading) contains the phrase "science of a Type II civilization." This got me to thinking: although we intuitively know what this means, does this actually tell us anything? After all, the only requirement to advance on the Kardashev scale is to have the capability to harness a particular amount of energy. What does that tell us about their medical or fundamental physics knowledge?

It seems to me that it would require no more knowledge than we have today to construct a Dyson Sphere to harness the energy of the Sun (which would make us a Type II civilization regardless of whether we actually use that much energy, as Isaac pointed out). Although the will is not there, the capacity certainly is.

Compare this to the future as depicted by Star Trek, for example. They (humans) are most likely a type I (the Enterprise is stated to generate on the order of $10^{12}~\text{W}$, vs. the $10^{16}~\text{W}$ required for a Type I, so their civilization as a whole is probably just over Type I), and they regard the Dyson sphere from that one episode as an impressive accomplishment, on as scale which they previously considered to be theoretical. This is despite the fact that they're zipping around the galaxy with space wizard magic advanced technology far beyond our current understanding of physics.

The Question

What level of development is required to reach Type $n\in\left\{1,2,3\right\}$ on the Kardashev scale (using Sagan's definition)? Put another way, what knowledge is absolutely necessary to harness the requisite amounts of power? Areas of knowledge that you may consider include, but are not limited to:

You can also discuss knowledge that may not be necessary to harness planetary/stellar/galactic amounts of energy, but must, or will almost certainly be learned beforehand. (For example, perhaps a certain knowledge of sociology would be gained in the course of coordinating a project on such a large scale.)

$\begingroup$Actually, the Kardashev scale is about the capability to harness energy on increasing scales, not necessarily the need to use it. Case in point: a Dyson sphere is used as an example of a type II civilization, but it will certainly radiate waste heat from the central star, meaning that there is energy available for use that isn't being captured. Sagan operates on purely a net energy requirement/production calculation. It's possible future tech will have evolved with significantly lower power requirements (look at the leaps and bounds with computers).$\endgroup$
– Isaac KotlickyApr 2 '15 at 19:30

3

$\begingroup$Also the Kardashev scale is about energy consumption regardless of source. It is not necessary that the energy come from the civilization's home world's sun; just that the sum of the energy consumed by all of the members of that civilization meets or exceeds the total energy potential of their home world's sun. Star Trek hand waves a great deal of their space-wizard-magic by way of their di-lithium/anti-matter engines. With a fleet of these monstrously powerful vessels and all their member worlds' power-generation/power-consumption levels, the Federation is easily Type II.$\endgroup$
– Henry TaylorApr 2 '15 at 19:49

$\begingroup$Michio Kaku said that we'll reached type I status in the next century and we'll be harnessing and controlling earthquake, typhoon... etc actually we're close to it then we know the internet and cellphone shrinks the world into a small islet. It is the energy storage that is denying us our status, imagine what potential it holds when you can have Ironman's Arc reactor, as for type II you will have to envelop entire Sun with solar panels and it is not a small feat.$\endgroup$
– user6760Apr 3 '15 at 0:40

$\begingroup$@IsaacKotlicky You seem to understand exactly what I was going for =) Even though we don't have the need to use 100 PW of power, don't we still have the capability to put solar panels all over the planet, making us Type I? I guess the question you raise is, is it enough to have the knowledge to advance on the Kardashev scale, or must you have the resources as well?$\endgroup$
– 2012rcampionApr 3 '15 at 13:33

$\begingroup$@2012rcampion actually, covering the earth with solar panels won't make us type 1, because there are other energy sources on the planet then the solar energy received from the Sun.$\endgroup$
– Isaac KotlickyApr 3 '15 at 13:36

4 Answers
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I've spent a good deal of time thinking about this and related problems. The puzzle caused by the multidimensional linkages between growth and technological progress has been a difficult one to crack. You can look up the giants in the field of growth, such as Solow, Ramsey, Simon, Harrod, as well as the New Growth Theory.

Production Possibilities Frontier

I chose this because it illustrates beautifully the difference between efficiency improvements of existing technology (which, at best, can get you to the PPC) and the shift to new PPFs through the discovery and implementation of new technology.

Here's a practical example (notice the inverted Y cost scale):

General Purpose Technologies as Gamechangers

This should go without saying, but in reality, this frontier is a hypersphere. The Hypersphere of Human Possibility, if you want to sound a bit grandiose about it. Imagine new technologies as little pins that push outward at the frontier. Now most technologies (say the little cardboard coffee-holders at starbucks) are not that impactful, and only push the frontier outward a little locally. Other technologies such as the combustion engine, electricity or computers are different -- these technologies have a virtually limitless range of applicability - they can push the frontier outward in many directions at once, and by a lot.

Even more interestingly, one such gamechanger can open the path towards another. Combustion engines were used to generate cheap electricity, and eventually cheap electricity was used to construct delicate electrical equipment, such as computers. Computers then were used to design better combustion engines, power distribution grids, better computers etc.

Visibility of New Technological Possibilities

The fundamental question is whether there will ever be diminishing marginal returns to new technological research.

In other words, was it just blind luck that each gamechanger opened the PPF towards accessing the next PPF-expanding gamechanger, or is this reinforcing nature a fixture of human progress? In other words, is it possible that we'll reach an area where the next gamechanger is forever out of reach of our most advanced PPF, say in the way Fusion power always seems to be 50 years away? This could be the case if some technological insight requires, say, an IQ beyond the reach of humans, or energy density levels unattainable with the most advanced technology.

Our history so far seems to indicate that if there are diminishing returns, we are far, far from reaching them. The key concept here is the visibility of new technologies. For instance, consider the brilliant leaps of insight achievable by genius: Leonardo Da Vinci could use concepts extant in his world to imagine flying machines and tanks, concepts centuries beyond his society's energy-wise capability to implement. Despite that, these were visible to Da Vinci.
By contrast, no matter how brilliant Da Vinci was, he literally had no chance of inventing quantum chromodynamics, because the prerequisite nearby intellectual assets were outside of his PPF. It was only through the employment of more energy-intensive means of reality manipulation and measurement that the discovery of the subtle aspects of reality embodied in QCD literally became conceivable. QCD was invisible to Da Vinci. This finally puts us in a position where we can answer your question.

New Technological Progress and Vantage Points on the Path to Kardashev level I

Reaching Kardashev Type I (10¹⁶W) is a hugely ambitious goal, since it would mean boosting our current energy resources by a factor of about 10,000. This is already so far outside our PPF that it is hard to even imagine. How would the world look like if, ceteris paribus, instead of an average US power consumption of 10.0 kW (which is essentially at the current frontier), we would average 100.0 MW? Essentially, you'd have the power of a Nimitz-class aircraft carrier in the hands of Joe Everybody, and that's not taking into account future efficiency gains, which are likely to be considerable as well. Think about it, the power that the most powerful nation on the planet wields (there's only a dozen or so of these behemoths in the world), would be at the fingertips of your average Joe.

This itself would be a greater leap than we've made in all history so far: from a basal metabolic rate of 100W, we got to 10,000 W at the frontier, most of it used to power industrial machines and robotic helpers. In reality, ceteris paribus would not hold, of course, so for instance human population will likely increase greatly before we reach Kardashev I, so the the per capita amount will likely be lower when we reach that threshold, although inequalities in distribution might mean that individuals might have access to levels far above that sooner.

Currently, there is an exploding PPF dimension, where expansion has not slowed for decades:

The implications of this relentless progress in the most scarce resource of all, namely intelligence, are surely vast yet their true scale and the new vantage points sure to be opened by them remain unfathomable. Even a marginally human-like special-purpose artificial intellect would change everything, probably more so than all the previous revolutions combined.

So, even on the path to K-I, there are gamechanging future technologies that we have visibility of, such as fusion power, competent dedicated as well as general purpose AIs, and full-blown nanotechnology. All three are massive game-changers in the energy, knowledge and manufacturing dimensions, which might help explain their relatively easy visibility from our vantage. There are sure to be countless others that remain invisible, some among them gamechangers.

None of these technologies are literally required for attaining Kardashev-I (as the OP mentions, in theory we could reach it with something much like current technology), but it is extremely unlikely that with massive boosts in available energy and the new vantages that opens such innovations will not be pursued, as they will appear as low-hanging fruit in that new context. Having been pursued, they will open a virtuous cycle of making new gains in energy harvesting possible, better computation etc., in turn making yet other potential technologies appear as low hanging fruit, and so ad infinitum or until the marginal rate of return becomes 0.

The scales are fairly similar for each component you mention: simply, as you have a greater understanding of all of those fields, you are able to harness more and more energy.

The fields you mention have a sort-of order of fundamentality. Engineering is impossible without physics; physics is impossible without mathematics (as are many of the soft sciences). So, essentially, the greater your understanding of mathematics, the more energy you are able to harness.

To put that another way, you can have Einstein and Newton and all the famous physicists and combine their brains, but unless you also have some mathematicians working out their principles, your scientists can't do anything significant.

To me, the "soft" sciences aren't so necessary here. Power is all about physics, not people: knowing how someone's brain understands and remembers all the physics isn't going to help you build a giant star-generator. The rest will develop at a similar rate, but with the more specialized/less fundamental fields lagging behind a bit. Adding to that, since power harnessing relies on engineering, power harnessing ability can never rise above the level of engineering, and will probably follow the pattern of lagging behind a bit. For your convenience, I shall provide a bar chart:

If we put some lines across that to represent Kardashev levels, we can see that it is even possible for a civilization to have mathematics one or conceivably even two levels above their civilization's level:

This does explain your Star Trek point: perhaps the technologies that enable them to zip across the universe so quickly have been refined through physics and engineering so they don't actually use that much power: thus, the power required is still in their power available to harvest. They have been able to refine this technology because they have knowledge of physics and engineering more advanced than their ability to harness power. Probably they set their scientists onto developing interstellar travel instead of power generation.

$\begingroup$I think you're sort of missing my point here... We observe these relative levels of development today (but not in the past; the Romans had advanced engineering knowledge while believing rocks fell because they liked being on the ground), and they will probably be the case for real-world civilizations. However, do we really need to know about Riemann manifolds or Lorentz transforms to reach Type I? I suspect the answer is no, and that the minimal development levels should have Maths lowest and POWER HARNESSED highest.$\endgroup$
– 2012rcampionApr 3 '15 at 14:04

$\begingroup$@2012rcampion Possibly; however, I can't accept that mathematical development would be lower than power harnessed development. You need at least a similar level in maths and physics and engineering to get up to x point on power harnessed.$\endgroup$
– ArtOfCodeApr 3 '15 at 14:06

$\begingroup$I guess it depends on how you look at it... I would consider 'calculus' to be roughly on par with 'orbital dynamics' on your y-axes, but Kepler discovered and formulated his laws using only analytic geometry, which I'd consider to be below calculus in development. Sure it would be a pain if you couldn't use calc in trajectory planning, but it wouldn't be impossible, right? After all, Euler's method for solving differential equations is just arithmetic, so if you have a version of Newton's laws you can simulate physical systems without calculus.$\endgroup$
– 2012rcampionApr 3 '15 at 14:14

$\begingroup$@2012rcampion True enough. I guess I've written this as how most new developments work (i.e. requiring a similar level of more fundamental fields) instead of including the exceptions like Kepler$\endgroup$
– ArtOfCodeApr 3 '15 at 14:20

$\begingroup$How do you directly compare any of these things? I think you can say 'a certain amount of math is needed for the development of certain science', but ultimately it's still a comparison of apples to oranges. I'd also question the amount of lag you're predicting here. Lagging 1.5 Kardashev levels between math and power harnessed would be the equivalent of developing all of modern math + a few hundred years while still at the power consumption levels of ancient Rome.$\endgroup$
– ckerschApr 3 '15 at 14:36

Many structures do not scale very well. One of the most classic issues is the square-cubed law which limits the ability for an entity to grow past a certain size. It if wants to be larger, it needs to have less density. However, lower density makes one unacceptable to all sorts of physics (like sandstorms).

Differing in opinion from ArtOfCode's answer, I would argue that the larger a society gets, the more its soft and hard sciences become harder to distinguish. The soft sciences have to be more codified (like hard sciences) to ensure the messages of the soft sciences do not get distorted with the weaker connections associated with lower density. Meanwhile, the hard sciences have to get more and more complicated, until they start looking like soft sciences. For a comparison, take a look at a naive CFD application which uses Navier-Stokes on a fixed grid. It is a very hard-science style approach. Now look at a modern high performance CFD designed to answer real questions about air flow through turbines. They often use things like Vortex Energy models which, when you read about them, start to look more like a soft science (particularly regarding transitions between where more traditional models do a better job and where the Vortex Energy approaches do a better job).

As an example, consider one facet of a civilization: composites:

Class < I: We play with composites, but steel and concrete still form the backbone of our civilization's construction. One could argue both steel and concrete are composites, but they are very simple ones.

Class I: It's really hard to reach class I by actually consuming all the energy that hits your planet. It's much easier to reach out into space and build solar collection there. Steel is nice here, but its a pain to haul up from the planet in any large quantities, so you'd make use of what you have available. Given that it is unlikely that we'll find enough iron-bearing asteroids to make this happen, we'll turn to less useful materials, and need to make them useful. Composites are a great way to get the best properties from multiple materials, so it sort of becomes a necesity here.

Class II: When you start talking about dyson spheres, you're really pushing at the limits of the tensile strengths of your materials. You start needing composites. You also start needing a good way to maintain all that material, because you can't just have a modern American density of people all the way around (it starts pushing against the square-cubed law again). Accordingly, not only do you need composites, but you start to need composites that heal themselves, like the enamel of our teeth.

Class III: At this point, the sheer number of atoms needed starts to become a limiting factor, driving us to even more sparse approaches. I can't even fathom what sorts of materials will be called upon here, webs of space dust or thin tendrils of dark matter. Simply no idea.

Or consider biology:

Class < I: Biology is neat. We learn a lot from it.

Class I: We need to really understand our biology, because we're starting to become the ecosystem, instead of being part of it.

Class II: Biology now becomes an artform, the fine art of constructing the self-repairing structures using what we understand from a few million years of evolution. Biological constructs here literally show signs of the individual groups that made them, because they're an art not a science.

Class III: Biology becomes nothing more than a working platform for a larger theory that can create biological-like creatures over the empty lightyears. Nobody actually uses amino acids, but there may be some information stored on how they once worked.

Who needs advanced development? Establish loads of bases at Type 1.5-2 level in solar systems and keep establishing them and you can get a type 2-2.5 society. And also, in the Kardashev scale, the energy harnessed should be multiplied by how efficiently they use the energy (i.e. how much work they can do), so high-tech, low power equipment contributes significantly.

$\begingroup$There’s a question (which I can’t find now) about growing a Dyson Sphere like a plant. If it’s just unmaintained kudzu, it doesn’t take any society at all!$\endgroup$
– JDługoszAug 7 '16 at 14:21

$\begingroup$@JDługosz I think it was about actual societies, not unmaintained self-growing dyson Spheres.$\endgroup$
– MathmagicianAug 14 '16 at 3:12